From 51f46b5e2a2a6eb1b73f635cecccac10f3d8d289 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Wed, 6 Jul 2016 21:16:17 -0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Johnson, M.E.}
\index{Rogers, C.}
\index{Schief, W.K.}
\index{Seiler, W.M.}
\begin{chunk}{axiom.bib}
@article{John94,
author = "Johnson, M.E. and Rogers, C. and Schief, W.K. and Seiler, W.M.",
title = "On moving pseudospherical surfaces: a generalised Weingarten
system and its formal analysis",
journal = "Lie Groups Appl.",
volume = "1",
pages = "124-136",
year = "1994",
keywords = "axiomref",
abstract =
"The connection between the motion of certain curves in $\mathbb{R}^3$
and $1+1$-dimensional soliton equations is by now well-established. On the
other hand, the sine-Gordon and other integrable equations may be
readily derived via the classical geometry of stationary
pseudospherical surfaces. Here, the motion of pseudospherical surfaces
$S$ is considered in a natural orthonormal triad formulation. In one case,
in a motion in which the Gaussian curvature of $S$ remains constant in
time, an integrable nonlinear evolution equation is derived which has
its origin in the description of wave propagation in an anharmonic
crystal. In a second case, wherein the Gaussian curvature is allowed
to vary in time, a classical generalised Weingarten system is derived
in connection with the purely normal propagation of a pseudospherical
surface. This is linked to triply orthogonal coordinate systems of
Bianchi type. The generalised Weingarten system incorporates an
integrable $2+1$-dimensional sine-Gordon equation. The arbitrariness of the
solutions of the generalised Weingarten system is determined via a
completion procedure."
}
\end{chunk}
\index{Kajler, Norbert}
\index{Soiffer, Neil}
\begin{chunk}{axiom.bib}
author = "Kajler, Norbert and Soiffer, Neil",
title = "Some human interaction issues in computer algebra",
journal = "SIGSAM Bulletin",
volume = "28",
number = "1",
pages = "18-28",
year = "1994",
abstract =
"This paper addresses some of the current issues concerning the
improvement of user interfaces for computer algebra systems. Some
state of the art commercial software as well as research prototypes
are presented, followed by a description of present research
directions."
}
\end{chunk}
\index{Kripfganz, Jochen}
\index{Perlt, Holger}
\begin{chunk}{axiom.bib}
@misc{Krip94,
author = "Kripfganz, Jochen and Perlt, Holger",
title = "Working with Mathematica. An Introduction with examples",
comment = "Arbeiten mit Mathematica. Eine Einfuhrung mit Beispielen",
book = "Hander",
year = "1994",
keywords = "axiomref"
}
\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@InProceedings{Schw94,
author = "Schwarz, Fritz",
title = "Computer algebra software for scientific applications",
booktitle = "Computerized symbolic manipulation in mechanics",
year = "1994",
publisher = "Springer-Verlag",
pages = "67-117",
series = "CISM Courses Lecture 343",
keywords = "axiomref",
abstract =
"The central subject of this article are two basic questions: How to
make the process of developing computer algebra software on a large
scale ($10^4 to $10^5$) lines of code or more) more efficient and
how to improve the quality of the result. Taking procedures from well
established engineering sciences as a guide, two fundamental
principles turned out to be of overwhelming importance: Modularization
and limitation of growth through reuse. Important means for achieving
these goals turned out to be concept of an abstract data type and the
principles of object-oriented design. It is advocated to install an
additional abstraction level between the mathematics and the machine
in order to render it possible to develop (computer algebra) system
independent mathematical software. Basic constituents of this level
are a type system and a high-level language."
}
\end{chunk}
\index{Kajler, Norbert}
\begin{chunk}{axiom.bib}
@article{Kajl92,
author = "Kajler, Norbert",
title = "CAS/PI: a Portable and Extensible Interface for Computer
Algebra Systems",
year = "1992",
booktitle = "Proc. ISSAC 1992",
series = "ISSAC 1992",
pages = "376-386",
isbn = "0-89791-489-9 (soft cover) 0-89791-490-2 (hard cover)",
keywords = "axiomref",
paper = "Kajl92.pdf",
abstract =
"CAS/$\pi$ is a Computer Algebra System graphic user interface
designed to be highly portable and extensible. It has been developed
by composition of pre-existing software tools such as Maple, Sisyphe,
or Ulysse systems, ZicVis 3-D plotting library, etc, using control
integration technology and a set of high level graphic toolkits to
build the formula editor and the dialog manager. The main aim of
CAS/$\pi$ is to allow a wide range of runtime recon gurations and
extensions. For instance, it is possible to add new tools to a running
system, to modify connections between working tools, to extend the set
of graphic symbols managed by the formula editor, to design new high
level editing commands based on the syntax or semantics of
mathematical formulas, to customize and extend the menu-button based
user interface, etc. More generally, CAS/$\pi$ can be seen equally as
a powerful system-independent graphic user interface enabling
inter-systems communications, a toolkit to allow fast development of
custom-made scientific software environments, or a very convenient
framework for experimenting with computer algebra systems protocols
and man-machine interfaces."
}
\end{chunk}
\index{Schu, J.}
\index{Seiler, Werner Markus}
\index{Calmet, Jacques}
\begin{chunk}{axiom.bib}
@InProceedings{Schu92,
author = "Schu, J. and Seiler, Werner Markus and Calmet, Jacques",
title = "Algorithmic Methods For Lie Pseudogroups'",
booktitle = "Proc. Modern Group Analysis: Advanced Analytical and
Computational Methods in Mathematical Physics",
pages = "337-344",
location = "Acireale (Italy)",
year = "1992",
publisher = "Kluwer",
url =
"http://www.iks.kti.edu/fileadmin/User/calmet/papers/Acireale-93.ps.gz",
keywords = "axiomref"
}
\end{chunk}
\index{Seiler, Werner Markus}
\begin{chunk}{axiom.bib}
@article{Seil99,
author = "Seiler, Werner Markus",
title = "DETools: A Library for Differential Equations",
paper = "Seil99.pdf",
year = "1999",
keywords = "axiomref",
abstract =
"This article tries to give at least a brief introduction. The MuPAD
library is extended on two levels. The first one consists of a new
library detools containing a number of routines for treating
differential equations. This includes support for the graphical
presentation of the output of the numerical routines in MuPAD, some
methods for analysing or generating differential equations and also
routines for solving some classes of partial differential
equations. The use of this new library will be described in this
article. The second level is somewhat more advanced and requires a
certain familiarity with the object-oriented domains."
}
\end{chunk}
\index{Bradford, Russell}
\index{Davenport, James H.}
\index{England, Matthew}
\index{McCallum, Scott}
\index{Wilson, David}
\begin{chunk}{axiom.bib}
@misc{Brad15,
author = "Bradford, Russell and Davenport, James H. and England, Matthew and
McCallum, Scott",
title = "Truth Table Invariant Cylindrical Algebraic Decomposition",
url = "https://arxiv.org/pdf/1401.0645.pdf",
paper = "Brad15.pdf",
year = "2015",
abstract =
"When using cylindrical algebraic decomposition (CAD) to solve a
problem with respect to a set of polynomials, it is likely not the
signs of those polynomials that are of paramount importance but rather
the truth values of certain quantifier free formulae involving
them. This observation motivates our article and definition of a Truth
Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors
presented an algorithm that can efficiently and directly construct a
TTICAD for a list of formulae in which each has an equational
constraint. This was achieved by generalising McCallum's theory of
reduced projection operators. In this paper we present an extended
version of our theory which can be applied to an arbitrary list of
formulae, achieving savings if at least one has an equational
constraint. We also explain how the theory of reduced projection
operators can allow for further improvements to the lifting phase of
CAD algorithms, even in the context of a single equational constraint.
The algorithm is implemented fully in Maple and we present both
promising results from experimentation and a complexity analysis
showing the benefits of our contributions."
}
\end{chunk}
\index{Bradford, Russell}
\index{Chen, Changbo}
\index{Davenport, James H.}
\index{England, Matthew}
\index{Maza, Marc Moreno}
\index{Wilson, David}
\begin{chunk}{axiom.bib}
@misc{Brad14,
author = "Bradford, Russell and Chen, Changbo and Davenport, James H. and
England, Matthew and Maza, Marc Moreno and Wilson, David",
title = "Truth Table Invariant Cylindrical Algebraic Decomposition by
Regular Chains",
url = "https://arxiv.org/pdf/1401.6310.pdf",
paper = "Brad14.pdf",
year = "2014",
abstract =
"A new algorithm to compute cylindrical algebraic decompositions
(CADs) is presented, building on two recent advances. Firstly, the
output is truth table invariant (a TTICAD) meaning given formulae have
constant truth value on each cell of the decomposition. Secondly, the
computation uses regular chains theory to first build a cylindrical
decomposition of complex space (CCD) incrementally by polynomial.
Significant modification of the regular chains technology wa s used to
achieve the more sophisticated invariance criteria. Experimental
results on an implementation in the {\tt RegularChains} Library for Maple
verify that combining these advances gives an algorithm superior to
its individual components and competitive with the state of the art."
}
\end{chunk}
\index{Wilson, David}
\index{Bradford, Russell}
\index{Davenport, James H.}
\index{England, Matthew}
\begin{chunk}{axiom.bib}
@misc{Wils14,
author = "Wilson, David and Bradford, Russell and Davenport, James H. and
England, Matthew",
title = "Cylindrical Algebraic Sub-Decompositions",
url = "https://arxiv.org/pdf/1401.0647.pdf",
paper = "Wils14.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decompositions (CADs) are a key tool in real
algebraic geometry, used primarily for eliminating quantifiers over
the reals and studying semi-algebraic sets. In this paper we
introduce cylindrical algebraic sub-decompositions (sub-CADs), which
are subsets of CADs containing all the information needed to specify a
solution for a given problem. We define two new types of sub-CAD:
variety sub-CADs which are those cells in a CAD lying on a designated
variety; and layered sub-CADs which have only those cells of
dimension higher than a specified value. We present algorithms to
produce these and describe how the two approaches may be combined with
each other and the recent theory of truth-table invariant CAD. We
give a complexity analysis showing that these techniques can offer
substantial theoretical savings, which is supported by experimentation
using an implementation in Maple."
}
\end{chunk}
\index{England, Matthew}
\index{Wilson, David}
\index{Bradford, Russell}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@misc{Engl14,
author = "England, Matthew and Wilson, David and Bradford, Russell and
Davenport, James H.",
title = "Using the Regular Chains Library to build cylindrical algebraic
decompositions by projecting and lifting",
url = "https://arxiv.org/pdf/1405.6090.pdf",
paper = "Engl14.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decomposition (CAD) is an important tool, both
for quantifier elimination over the reals and a range of other
applications. Traditionally, a CAD is built through a process of
projection and lifting to move the problem within Euclidean spaces of
changing dimension. Recently, an alternative approach which first
decomposes complex space using triangular decomposition before
refining to real space has been introduced and implemented within the
Regular-Chains Library of Maple. We here describe a freely available
package ProjectionCAD which utilises the routines within the
RegularChains Library to build CADs by projection and lifting. We
detail how the projection and lifting algorithms were modified to
allow this, discuss the motivation and survey the functionality of the
package."
}
\end{chunk}
\index{England, Matthew}
\index{Bradford, Russell}
\index{Davenport, James H.}
\index{Wilson, David}
\begin{chunk}{axiom.bib}
@misc{Engl14a,
author = "England, Matthew and Bradford, Russell and Davenport, James H. and
Wilson, David",
title = "Choosing a variable ordering for truth-table invariant cylindrical
algebraic decomposition by incremental triangular decomposition",
url = "https://arxiv.org/pdf/1405.6094.pdf",
paper = "Engl14a.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decomposition (CAD) is a key tool for solving
problems in real algebraic geometry and beyond. In recent years a new
approach has been developed, where regular chains technology is used
to first build a decomposition in complex space. We consider the
latest variant of this which builds the complex decomposition
incrementally by polynomial and produces CADs on whose cells a
sequence of formulae are truth-invariant. Like all CAD algorithms the
user must provide a variable ordering which can have a profound impact
on the tractability of a problem. We evaluate existing heuristics to
help with the choice for this algorithm, suggest improvements and then
derive a new heuristic more closely aligned with the mechanics of the
new algorithm."
}
\end{chunk}
\index{England, Matthew}
\index{Bradford, Russell}
\index{Chen, Changbo}
\index{Davenport, James H.}
\index{Maza, Marc Moreno}
\index{Wilson, David}
\begin{chunk}{axiom.bib}
@misc{Engl14b,
author = "England, Matthew and Bradford, Russell and Chen, Changbo and
Davenport, James H. and Maza, Marc Moreno",
title = "Problem formulation for truth-table invariant cylindrical
algebraic decomposition by incremental triangular decomposition",
url = "https://arxiv.org/pdf/1404.6371.pdf",
paper = "Engl14b.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decompositions (CADs) are a key tool for
solving problems in real algebraic geometry and beyond. We recently
presented a new CAD algorithm combining two advances: truth-table
invariance, making the CAD invariant with respect to the truth of
logical formulae rather than the signs of polynomials; and CAD
construction by regular chains technology, where first a complex
decomposition is constructed by refining a tree incrementally by
constraint. We here consider how best to formulate problems for input
to this algorithm. We focus on a choice (not relevant for other CAD
algorithms) about the order in which constraints are presented. We
develop new heuristics to help make this choice and thus allow the
best use of the algorithm in practice. We also consider other choices
of problem formulation for CAD, as discussed in CICM 2013, revisiting
these in the context of the new algorithm."
}
\end{chunk}
\index{Chen, Changbo}
\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@misc{Chen12,
author = "Chen, Changbo and Maza, Marc Moreno",
title = "An Incremental Algorithm for Computing Cylindrical Algebraic
Decompositions",
url = "https://arxiv.org/pdf/1210.5543.pdf",
paper = "Chen12.pdf",
year = "2012",
abstract =
"In this paper, we propose an incremental algorithm for computing
cylindrical al gebraic decompositions. The algorithm consists of two
parts: computing a complex cylindrical tree and refining this complex
tree into a cylindrical tree in real space. The incrementality comes
from the first part of the algorithm, where a complex cylindrical tree
is constructed by refining a previous complex cylindrical tree with a
polynomial constraint. We have implemented our algorithm in Maple. The
experimentation shows that the proposed algorithm outperforms existing
ones for many examples taken from the literature"
}
\end{chunk}
---
books/bookvolbib.pamphlet | 410 ++++++++++-
changelog | 2 +
patch | 1608 +++++++++-------------------------------
src/axiom-website/patches.html | 2 +
4 files changed, 724 insertions(+), 1298 deletions(-)
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 5ec7407..e39c1ba 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -9940,6 +9940,73 @@ J. Symbolic Computation 5, 237-259 (1988)
\end{chunk}
+\index{Bradford, Russell}
+\index{Chen, Changbo}
+\index{Davenport, James H.}
+\index{England, Matthew}
+\index{Maza, Marc Moreno}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Brad14,
+ author = "Bradford, Russell and Chen, Changbo and Davenport, James H. and
+ England, Matthew and Maza, Marc Moreno and Wilson, David",
+ title = "Truth Table Invariant Cylindrical Algebraic Decomposition by
+ Regular Chains",
+ url = "https://arxiv.org/pdf/1401.6310.pdf",
+ paper = "Brad14.pdf",
+ year = "2014",
+ abstract =
+ "A new algorithm to compute cylindrical algebraic decompositions
+ (CADs) is presented, building on two recent advances. Firstly, the
+ output is truth table invariant (a TTICAD) meaning given formulae have
+ constant truth value on each cell of the decomposition. Secondly, the
+ computation uses regular chains theory to first build a cylindrical
+ decomposition of complex space (CCD) incrementally by polynomial.
+ Significant modification of the regular chains technology wa s used to
+ achieve the more sophisticated invariance criteria. Experimental
+ results on an implementation in the {\tt RegularChains} Library for Maple
+ verify that combining these advances gives an algorithm superior to
+ its individual components and competitive with the state of the art."
+}
+
+\end{chunk}
+
+\index{Bradford, Russell}
+\index{Davenport, James H.}
+\index{England, Matthew}
+\index{McCallum, Scott}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Brad15,
+ author = "Bradford, Russell and Davenport, James H. and England, Matthew and
+ McCallum, Scott",
+ title = "Truth Table Invariant Cylindrical Algebraic Decomposition",
+ url = "https://arxiv.org/pdf/1401.0645.pdf",
+ paper = "Brad15.pdf",
+ year = "2015",
+ abstract =
+ "When using cylindrical algebraic decomposition (CAD) to solve a
+ problem with respect to a set of polynomials, it is likely not the
+ signs of those polynomials that are of paramount importance but rather
+ the truth values of certain quantifier free formulae involving
+ them. This observation motivates our article and definition of a Truth
+ Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors
+ presented an algorithm that can efficiently and directly construct a
+ TTICAD for a list of formulae in which each has an equational
+ constraint. This was achieved by generalising McCallum's theory of
+ reduced projection operators. In this paper we present an extended
+ version of our theory which can be applied to an arbitrary list of
+ formulae, achieving savings if at least one has an equational
+ constraint. We also explain how the theory of reduced projection
+ operators can allow for further improvements to the lifting phase of
+ CAD algorithms, even in the context of a single equational constraint.
+ The algorithm is implemented fully in Maple and we present both
+ promising results from experimentation and a complexity analysis
+ showing the benefits of our contributions."
+}
+
+\end{chunk}
+
\index{Brown, Christopher W.}
\begin{chunk}{axiom.bib}
@phdthesis{Brow99,
@@ -10024,12 +10091,15 @@ J. Symbolic Computation 5, 237-259 (1988)
\end{chunk}
\index{Brown, Christopher W.}
-\begin{chunk}{ignore}
-\bibitem[Brown 02]{Brow02} Brown, Christopher W.
- title = "QEPCAD B -- A program for computing with semi-algebraic sets using CADs",
+\begin{chunk}{axiom.bib}
+@misc{Brow02,
+ author = "Brown, Christopher W.",
+ title = "QEPCAD B -- A program for computing with semi-algebraic sets
+ using CADs",
paper = "Brow02.pdf",
- abstract = "
- This report introduces QEPCAD B, a program for computing with real
+ year = "2002",
+ abstract =
+ "This report introduces QEPCAD B, a program for computing with real
algebraic sets using cylindrical algebraic decomposition (CAD). QEPCAD
B both extends and improves upon the QEPCAD system for quantifier
elimination by partial cylindrical algebraic decomposition written by
@@ -10040,6 +10110,31 @@ J. Symbolic Computation 5, 237-259 (1988)
most of the extended features of QEPCAD B, but improvements to the
basic CAD implementation and to the SACLIB library on which QEPCAD is
based are the results of many people's work."
+}
+
+\end{chunk}
+
+\index{Chen, Changbo}
+\index{Maza, Marc Moreno}
+\begin{chunk}{axiom.bib}
+@misc{Chen12,
+ author = "Chen, Changbo and Maza, Marc Moreno",
+ title = "An Incremental Algorithm for Computing Cylindrical Algebraic
+ Decompositions",
+ url = "https://arxiv.org/pdf/1210.5543.pdf",
+ paper = "Chen12.pdf",
+ year = "2012",
+ abstract =
+ "In this paper, we propose an incremental algorithm for computing
+ cylindrical al gebraic decompositions. The algorithm consists of two
+ parts: computing a complex cylindrical tree and refining this complex
+ tree into a cylindrical tree in real space. The incrementality comes
+ from the first part of the algorithm, where a complex cylindrical tree
+ is constructed by refining a previous complex cylindrical tree with a
+ polynomial constraint. We have implemented our algorithm in Maple. The
+ experimentation shows that the proposed algorithm outperforms existing
+ ones for many examples taken from the literature"
+}
\end{chunk}
@@ -10087,6 +10182,101 @@ J. Symbolic Computation 5, 237-259 (1988)
\end{chunk}
\index{England, Matthew}
+\index{Wilson, David}
+\index{Bradford, Russell}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@misc{Engl14,
+ author = "England, Matthew and Wilson, David and Bradford, Russell and
+ Davenport, James H.",
+ title = "Using the Regular Chains Library to build cylindrical algebraic
+ decompositions by projecting and lifting",
+ url = "https://arxiv.org/pdf/1405.6090.pdf",
+ paper = "Engl14.pdf",
+ year = "2014",
+ abstract =
+ "Cylindrical algebraic decomposition (CAD) is an important tool, both
+ for quantifier elimination over the reals and a range of other
+ applications. Traditionally, a CAD is built through a process of
+ projection and lifting to move the problem within Euclidean spaces of
+ changing dimension. Recently, an alternative approach which first
+ decomposes complex space using triangular decomposition before
+ refining to real space has been introduced and implemented within the
+ Regular-Chains Library of Maple. We here describe a freely available
+ package ProjectionCAD which utilises the routines within the
+ RegularChains Library to build CADs by projection and lifting. We
+ detail how the projection and lifting algorithms were modified to
+ allow this, discuss the motivation and survey the functionality of the
+ package."
+}
+
+\end{chunk}
+
+\index{England, Matthew}
+\index{Bradford, Russell}
+\index{Davenport, James H.}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Engl14a,
+ author = "England, Matthew and Bradford, Russell and Davenport, James H. and
+ Wilson, David",
+ title = "Choosing a variable ordering for truth-table invariant cylindrical
+ algebraic decomposition by incremental triangular decomposition",
+ url = "https://arxiv.org/pdf/1405.6094.pdf",
+ paper = "Engl14a.pdf",
+ year = "2014",
+ abstract =
+ "Cylindrical algebraic decomposition (CAD) is a key tool for solving
+ problems in real algebraic geometry and beyond. In recent years a new
+ approach has been developed, where regular chains technology is used
+ to first build a decomposition in complex space. We consider the
+ latest variant of this which builds the complex decomposition
+ incrementally by polynomial and produces CADs on whose cells a
+ sequence of formulae are truth-invariant. Like all CAD algorithms the
+ user must provide a variable ordering which can have a profound impact
+ on the tractability of a problem. We evaluate existing heuristics to
+ help with the choice for this algorithm, suggest improvements and then
+ derive a new heuristic more closely aligned with the mechanics of the
+ new algorithm."
+}
+
+\end{chunk}
+
+\index{England, Matthew}
+\index{Bradford, Russell}
+\index{Chen, Changbo}
+\index{Davenport, James H.}
+\index{Maza, Marc Moreno}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Engl14b,
+ author = "England, Matthew and Bradford, Russell and Chen, Changbo and
+ Davenport, James H. and Maza, Marc Moreno",
+ title = "Problem formulation for truth-table invariant cylindrical
+ algebraic decomposition by incremental triangular decomposition",
+ url = "https://arxiv.org/pdf/1404.6371.pdf",
+ paper = "Engl14b.pdf",
+ year = "2014",
+ abstract =
+ "Cylindrical algebraic decompositions (CADs) are a key tool for
+ solving problems in real algebraic geometry and beyond. We recently
+ presented a new CAD algorithm combining two advances: truth-table
+ invariance, making the CAD invariant with respect to the truth of
+ logical formulae rather than the signs of polynomials; and CAD
+ construction by regular chains technology, where first a complex
+ decomposition is constructed by refining a tree incrementally by
+ constraint. We here consider how best to formulate problems for input
+ to this algorithm. We focus on a choice (not relevant for other CAD
+ algorithms) about the order in which constraints are presented. We
+ develop new heuristics to help make this choice and thus allow the
+ best use of the algorithm in practice. We also consider other choices
+ of problem formulation for CAD, as discussed in CICM 2013, revisiting
+ these in the context of the new algorithm."
+}
+
+\end{chunk}
+
+\index{England, Matthew}
\index{Bradford, Russell}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@@ -10200,6 +10390,37 @@ J. Symbolic Computation 5, 237-259 (1988)
\end{chunk}
+\index{Wilson, David}
+\index{Bradford, Russell}
+\index{Davenport, James H.}
+\index{England, Matthew}
+\begin{chunk}{axiom.bib}
+@misc{Wils14,
+ author = "Wilson, David and Bradford, Russell and Davenport, James H. and
+ England, Matthew",
+ title = "Cylindrical Algebraic Sub-Decompositions",
+ url = "https://arxiv.org/pdf/1401.0647.pdf",
+ paper = "Wils14.pdf",
+ year = "2014",
+ abstract =
+ "Cylindrical algebraic decompositions (CADs) are a key tool in real
+ algebraic geometry, used primarily for eliminating quantifiers over
+ the reals and studying semi-algebraic sets. In this paper we
+ introduce cylindrical algebraic sub-decompositions (sub-CADs), which
+ are subsets of CADs containing all the information needed to specify a
+ solution for a given problem. We define two new types of sub-CAD:
+ variety sub-CADs which are those cells in a CAD lying on a designated
+ variety; and layered sub-CADs which have only those cells of
+ dimension higher than a specified value. We present algorithms to
+ produce these and describe how the two approaches may be combined with
+ each other and the recent theory of truth-table invariant CAD. We
+ give a complexity analysis showing that these techniques can offer
+ substantial theoretical savings, which is supported by experimentation
+ using an implementation in Maple."
+}
+
+\end{chunk}
+
\section{Comparison of Computer Algebra System} %%%%%%%%%%%%%%%%%%%%%%
\index{Bernardin, Laurent}
@@ -17000,6 +17221,42 @@ Draft September 5, 1988
\end{chunk}
+\index{Johnson, M.E.}
+\index{Rogers, C.}
+\index{Schief, W.K.}
+\index{Seiler, Werner Markus}
+\begin{chunk}{axiom.bib}
+@article{John94,
+ author = "Johnson, M.E. and Rogers, C. and Schief, W.K. and Seiler, W.M.",
+ title = "On moving pseudospherical surfaces: a generalised Weingarten
+ system and its formal analysis",
+ journal = "Lie Groups Appl.",
+ volume = "1",
+ pages = "124-136",
+ year = "1994",
+ keywords = "axiomref",
+ abstract =
+ "The connection between the motion of certain curves in $\mathbb{R}^3$
+ and $1+1$-dimensional soliton equations is by now well-established. On the
+ other hand, the sine-Gordon and other integrable equations may be
+ readily derived via the classical geometry of stationary
+ pseudospherical surfaces. Here, the motion of pseudospherical surfaces
+ $S$ is considered in a natural orthonormal triad formulation. In one case,
+ in a motion in which the Gaussian curvature of $S$ remains constant in
+ time, an integrable nonlinear evolution equation is derived which has
+ its origin in the description of wave propagation in an anharmonic
+ crystal. In a second case, wherein the Gaussian curvature is allowed
+ to vary in time, a classical generalised Weingarten system is derived
+ in connection with the purely normal propagation of a pseudospherical
+ surface. This is linked to triply orthogonal coordinate systems of
+ Bianchi type. The generalised Weingarten system incorporates an
+ integrable $2+1$-dimensional sine-Gordon equation. The arbitrariness of the
+ solutions of the generalised Weingarten system is determined via a
+ completion procedure."
+}
+
+\end{chunk}
+
\index{Joswig, Rainer}
\begin{chunk}{ignore}
\bibitem[Rainer 14]{Rain14} Joswig, Rainer
@@ -17103,6 +17360,7 @@ SIGSAM Communications in Computer Algebra, 157 2006
\index{Kajler, Norbert}
\begin{chunk}{axiom.bib}
+@article{Kajl92,
author = "Kajler, Norbert",
title = "CAS/PI: a Portable and Extensible Interface for Computer
Algebra Systems",
@@ -17111,7 +17369,49 @@ SIGSAM Communications in Computer Algebra, 157 2006
series = "ISSAC 1992",
pages = "376-386",
isbn = "0-89791-489-9 (soft cover) 0-89791-490-2 (hard cover)",
- keywords = "axiomref"
+ keywords = "axiomref",
+ paper = "Kajl92.pdf",
+ abstract =
+ "CAS/$\pi$ is a Computer Algebra System graphic user interface
+ designed to be highly portable and extensible. It has been developed
+ by composition of pre-existing software tools such as Maple, Sisyphe,
+ or Ulysse systems, ZicVis 3-D plotting library, etc, using control
+ integration technology and a set of high level graphic toolkits to
+ build the formula editor and the dialog manager. The main aim of
+ CAS/$\pi$ is to allow a wide range of runtime recon gurations and
+ extensions. For instance, it is possible to add new tools to a running
+ system, to modify connections between working tools, to extend the set
+ of graphic symbols managed by the formula editor, to design new high
+ level editing commands based on the syntax or semantics of
+ mathematical formulas, to customize and extend the menu-button based
+ user interface, etc. More generally, CAS/$\pi$ can be seen equally as
+ a powerful system-independent graphic user interface enabling
+ inter-systems communications, a toolkit to allow fast development of
+ custom-made scientific software environments, or a very convenient
+ framework for experimenting with computer algebra systems protocols
+ and man-machine interfaces."
+}
+
+\end{chunk}
+
+\index{Kajler, Norbert}
+\index{Soiffer, Neil}
+\begin{chunk}{axiom.bib}
+@article{Kajl94,
+ author = "Kajler, Norbert and Soiffer, Neil",
+ title = "Some human interaction issues in computer algebra",
+ journal = "SIGSAM Bulletin",
+ volume = "28",
+ number = "1",
+ pages = "18-28",
+ year = "1994",
+ keywords = "axiomref",
+ abstract =
+ "This paper addresses some of the current issues concerning the
+ improvement of user interfaces for computer algebra systems. Some
+ state of the art commercial software as well as research prototypes
+ are presented, followed by a description of present research
+ directions."
}
\end{chunk}
@@ -17615,6 +17915,20 @@ ISSN 0304-3975
\end{chunk}
+\index{Kripfganz, Jochen}
+\index{Perlt, Holger}
+\begin{chunk}{axiom.bib}
+@misc{Krip94,
+ author = "Kripfganz, Jochen and Perlt, Holger",
+ title = "Working with Mathematica. An Introduction with examples",
+ comment = "Arbeiten mit Mathematica. Eine Einfuhrung mit Beispielen",
+ book = "Hander",
+ year = "1994",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Kumar, P.}
\index{Pellegrino, S.}
\begin{chunk}{axiom.bib}
@@ -17860,7 +18174,7 @@ CODEN JSYCEH ISSN 0747-7171
\end{chunk}
\index{Lambe, Larry A.}
-\index{Seiler, Werner M.}
+\index{Seiler, Werner Markus}
\begin{chunk}{axiom.bib}
@article{Lamb02,
author = "Lambe, Larry A. and Seiler, Werner M.",
@@ -19833,6 +20147,16 @@ In ACM [ACM89], pp17-25 ISBN 0-89791-325-6 LCCN QA76.95.I59 1989
\end{chunk}
\index{Schwarz, Fritz}
+\begin{chunk}{ignore}
+\bibitem[Schwarz 91]{Sch91} Schwarz, F.
+ title = "Monomial orderings and Gr{\"o}bner bases",
+SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic
+Manipulation) 2591) pp10-23 Jan. 1991 CODEN SIGSBZ ISSN 0163-5824
+ keywords = "axiomref",
+
+\end{chunk}
+
+\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@InProceedings{Schw02,
author = "Schwarz, Fritz",
@@ -19866,12 +20190,31 @@ In ACM [ACM89], pp17-25 ISBN 0-89791-325-6 LCCN QA76.95.I59 1989
\end{chunk}
\index{Schwarz, Fritz}
-\begin{chunk}{ignore}
-\bibitem[Schwarz 91]{Sch91} Schwarz, F.
- title = "Monomial orderings and Gr{\"o}bner bases",
-SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic
-Manipulation) 2591) pp10-23 Jan. 1991 CODEN SIGSBZ ISSN 0163-5824
+\begin{chunk}{axiom.bib}
+@InProceedings{Schw94,
+ author = "Schwarz, Fritz",
+ title = "Computer algebra software for scientific applications",
+ booktitle = "Computerized symbolic manipulation in mechanics",
+ year = "1994",
+ publisher = "Springer-Verlag",
+ pages = "67-117",
+ series = "CISM Courses Lecture 343",
keywords = "axiomref",
+ abstract =
+ "The central subject of this article are two basic questions: How to
+ make the process of developing computer algebra software on a large
+ scale ($10^4 to $10^5$) lines of code or more) more efficient and
+ how to improve the quality of the result. Taking procedures from well
+ established engineering sciences as a guide, two fundamental
+ principles turned out to be of overwhelming importance: Modularization
+ and limitation of growth through reuse. Important means for achieving
+ these goals turned out to be concept of an abstract data type and the
+ principles of object-oriented design. It is advocated to install an
+ additional abstraction level between the mathematics and the machine
+ in order to render it possible to develop (computer algebra) system
+ independent mathematical software. Basic constituents of this level
+ are a type system and a high-level language."
+}
\end{chunk}
@@ -19999,11 +20342,25 @@ in Calmet [Cal94] pp103-104
\end{chunk}
\index{Seiler, Werner Markus}
-\begin{chunk}{ignore}
-\bibitem[Seiler (a)]{Seixx} Seiler, W.M.
+\begin{chunk}{axiom.bib}
+@article{Seil99,
+ author = "Seiler, Werner Markus",
title = "DETools: A Library for Differential Equations",
- url = "http://iaks-www.ira.uka.de/iaks-calmet/werner/werner.html",
+ paper = "Seil99.pdf",
+ year = "1999",
keywords = "axiomref",
+ abstract =
+ "This article tries to give at least a brief introduction. The MuPAD
+ library is extended on two levels. The first one consists of a new
+ library detools containing a number of routines for treating
+ differential equations. This includes support for the graphical
+ presentation of the output of the numerical routines in MuPAD, some
+ methods for analysing or generating differential equations and also
+ routines for solving some classes of partial differential
+ equations. The use of this new library will be described in this
+ article. The second level is somewhat more advanced and requires a
+ certain familiarity with the object-oriented domains."
+}
\end{chunk}
@@ -20165,14 +20522,23 @@ LCCN QA76.76.A65 S95 1992
\end{chunk}
-\begin{chunk}{ignore}
-\bibitem[SSC92]{SSC92}.
+\index{Schu, J.}
+\index{Seiler, Werner Markus}
+\index{Calmet, Jacques}
+\begin{chunk}{axiom.bib}
+@InProceedings{Schu92,
+ author = "Schu, J. and Seiler, Werner Markus and Calmet, Jacques",
title = "Algorithmic Methods For Lie Pseudogroups'",
-In N. Ibragimov, M. Torrisi and A. Valenti, editors, Proc. Modern Group
-Analysis: Advanced Analytical and Computational Methods in Mathematical
-Physics, pp337-344, Acireale (Italy), 1992 Kluwer, Dordrecht 1993
- url = "http://iaks-www.ira.uka.de/iaks-calmet/werner/Papers/Acireale92.ps.gz",
- keywords = "axiomref",
+ booktitle = "Proc. Modern Group Analysis: Advanced Analytical and
+ Computational Methods in Mathematical Physics",
+ pages = "337-344",
+ location = "Acireale (Italy)",
+ year = "1992",
+ publisher = "Kluwer",
+ url =
+ "http://www.iks.kti.edu/fileadmin/User/calmet/papers/Acireale-93.ps.gz",
+ keywords = "axiomref"
+}
\end{chunk}
diff --git a/changelog b/changelog
index e7fa296..5107e24 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20160704 tpd src/axiom-website/patches.html 20160706.01.tpd.patch
+20160705 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiom-website/patches.html 20160705.01.tpd.patch
20160705 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiom-website/patches.html 20160704.04.tpd.patch
diff --git a/patch b/patch
index f339a05..6639aab 100644
--- a/patch
+++ b/patch
@@ -2,1341 +2,397 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
-\index{Schwardmann, Ulrich}
-\begin{chunk}{axiom.bib}
-@book{Schw95,
- author = "Schwardmann, Ulrich",
- title = "Computer algebra systems",
- comment = "Computeralgebra-Systeme, German",
- publisher = "Addison-Wesley",
- year = "1995",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Storme, L.}
-\index{van Maldeghem, H.}
-\begin{chunk}{axiom.bib}
-@article{Stor95,
- author = "Storme, L. and van Maldeghem, H.",
- title = "Cyclic caps in PG(3,q)",
- journal = "Geom. Dedicata",
- volume = "56",
- number = "3",
- pages = "271-284",
- year = "1995",
- keywords = "axiomref",
- url = "https://cage.ugent.be/~hvm/artikels/44.pdf",
- paper = "Stor95.pdf",
- abstract =
- "A $k$-cap $K$ on $PG(n,q)$ is a set of $k$ points, no three of which
- are collinear. $K$ is complete if it cannot be extended to a $k+1$
- cap. If $K$ is invariant under a cyclic subgroup (which acts regularly
- on $K$) of $PGL(n+1,q)$, the $K$ is cyclic.
-
- This article investigates cyclic complete $k$-caps in
- $PG(3,q). Namely, the different types of complete $k$-caps $K$ in
- $PG(3,q)$ stabilized by a cyclic projective group $G$ of order $k$,
- acting regularly on the points of $K$, are determined. We show that in
- $PG(3,q)$, $q$ even, the elliptic quadric is the only cyclic complete
- $k$-cap. For $q$ odd, it is shown that besides the elliptic quadric,
- there also exist cyclic $k$-caps containing $k/2$ points of two
- disjoint elliptic quadrics or two disjoint hyperbolic quadrics and
- that there exist cyclic $k$-caps stabilized by a transitive cyclic
- group $G$ fixed precisely one point and one plane of
- $PG(3,q)$. Concrete examples of such caps, found using AXIOM and
- CAYLEY, are presented."
-}
-
-\end{chunk}
-
-\index{Weber, Andreas}
-\begin{chunk}{axiom.bib}
-@article{Webe95,
- author = "Weber, Andreas",
- title = "On coherence in computer algebra",
- journal = "J. Symb. Comput.",
- volume = "19",
- number = "1-3",
- pages = "25-38",
- year = "1995",
- url =
-"http://cg.cs.uni-bonn.de/personal-pages/weber/publications/pdf/WeberA/Weber94e.pdf",
- paper = "Webe95.pdf",
- keywords = "axiomref",
- abstract = "
- Modern computer algebra systems (e.g. AXIOM) support a rich type
- system including parameterized data types and the possibility of
- implicit coercions between types. In such a type system it will be
- frequently the case that there are different ways of building
- coercions between types. An important requirement is that all
- coercions between two types coincide, a property which is called {\sl
- coherence}. We will prove a coherence theorem for a formal type system
- having several possibilities of coercions covering many important
- examples. Moreover, we will give some informal reasoning why the
- formally defined restrictions can be satisfied by an actual system."
-}
-
-\end{chunk}
-
-\index{Williamson, Clifton J.}
-\begin{chunk}{axiom.bib}
-@InProceedings{Will95,
- author = "Williamson, Clifton J.",
- title = "On the algebraic construction of tri-diagonal matrices with given
- characteristic polynomial",
- booktitle = "4th Conf. of Canadian Number Theory Association",
- year = "1995",
- location = "Halifax, Nova Scotia, Canada",
- pages = "417-431",
- keywords = "axiomref",
- paper = "Will95.pdf",
- abstract =
- "Let $K$ be a field of characteristic zero and assume
- \[f(x)=x^n-s_1x^{n-1}+\cdots+s_n \in L[x]\]
- where $L=K(s_1,\cdots,s_n)$. Call, for the purposes of this review, an
- $n\times n$ matrix 1-tridiagonal if its entries above and below the
- main diagonal are all 1, the entries on it are $d_1,\cdots,d_n$, and
- all other entries are 0. Under which conditions can
- $d_1,d_2,\cdots,d_n$ be chosen in a radical extension of $L$ such that
- the resulting 1-tridiagonal matrix has $f$ as its characteristic
- polynomial? The author’s answer: for $n=3$ always. The $d_i,s_i$
- are related by a system of algebraic equations of the form
- $\overline{f}_i(d_1,d_2,d_3)=s_i$. If this is satisfied, then by
- a resultant- or Groebner basis computation with respect to the
- lexicographic order, $d_3$ (say) must be a root of a certain
- irreducible polynomial $\varphi$ of degree 6. Joining this
- with a Galois group computation for $\varphi$ over $L$, it is shown
- that a solvable and necessarily transitive Gal($\varphi$) will be a
- necessary and sufficient condition for expressibility of $d_3$ (clear)
- and, thanks to the form of the Groebner basis, also of $d_1,d_2$ in
- radicals. Upon a discriminant computation of $\varphi$ and use of
- results of G. Butler and J. McKay [Commun. Algebra 11,
- 863-911 (1983; Zbl 0518.20003)] and J. McKay and L. Soicher [J. Number
- Theory 20, 273-281 (1985; Zbl 0579.12006)], this allows the author to
- deduce the mentioned result. For $n=4$, though the author cannot get as
- complete information about Galois groups etc., he can deduce e.g. that
- if $s_1,\cdots,s_4$ are algebraically independent over $\mathbb{Q}$,
- then $d_1,\cdots,d_4$ are not expressible in radicals over
- $\mathbb{Q}(s_1,\cdots,s_4)$. He mentions, however, a solvable subcase."
-}
-
-\end{chunk}
-
-\index{Bosma, Wieb}
-\index{Cannon, John}
-\index{Matthews, Graham}
-\begin{chunk}{axiom.bib}
-@InProceedings{Bosm94,
- author = "Bosma, Wieb and Cannon, John and Matthews, Graham",
- title = "Programming with algebraic structures: Design of the Magma
- language",
- booktitle = "Proc. ISSAC 94",
- series = "ISSAC 94",
+\index{Johnson, M.E.}
+\index{Rogers, C.}
+\index{Schief, W.K.}
+\index{Seiler, W.M.}
+\begin{chunk}{axiom.bib}
+@article{John94,
+ author = "Johnson, M.E. and Rogers, C. and Schief, W.K. and Seiler, W.M.",
+ title = "On moving pseudospherical surfaces: a generalised Weingarten
+ system and its formal analysis",
+ journal = "Lie Groups Appl.",
+ volume = "1",
+ pages = "124-136",
year = "1994",
- publisher = "ACM Press",
- location = "Baltimore, MD",
- pages = "52-57",
keywords = "axiomref",
- paper = "Bosm94.pdf",
- url = "http://www.math.ru.nl/~bosma/pubs/ISSAC94.pdf",
abstract =
- "MAGMA is a new software system for computational algebra, number
- theory and geometry whose design is centred on the concept of
- algebraic structure (magma). The use of algebraic structure as a
- design paradigm provides a natural strong typing mechanism. Further,
- structures and their morphisms appear in the language as first class
- objects. Standard mathematical notions are used for the basic data
- types. The result is a powerful, clean language which deals with
- objects in a mathematically rigorous manner. The conceptual and
- implementation ideas behind MAGMA will be examined in this paper. This
- conceptual base differs significantly from those underlying other
- computer algebra systems."
-}
-
-\end{chunk}
-
-\index{Dingle, Adam}
-\index{Fateman, Richard J.}
-\begin{chunk}{axiom.bib}
-@InProceedings{Ding94,
- author = "Dingle, Adam and Fateman, Richard",
- title = "Branch Cuts in Computer Algebra",
- year = "1994",
- booktitle = "Proc. ISSAC 1994",
- series = "ISSAC 94",
- url = "http://www.cs.berkeley.edu/~fateman/papers/ding.ps",
- paper = "Ding94.pdf",
- keywords = "axiomref",
- abstract =
- "Many standard functions, such as the logarithms and square root
- functions, cannot be defined continuously on the complex
- plane. Mistaken assumptions about the properties of these functions
- lead computer algebra systems into various conundrums. We discuss how
- they can manipulate such functions in a useful fashion."
-}
-
-\end{chunk}
-
-\index{Duval, Dominique}
-\index{Senechaud, Pascale}
-\begin{chunk}{axiom.bib}
-@article{Duva94d,
- author = "Duval, Dominique and Senechaud, Pascale",
- title = "Sketches and parametrization",
- journal = "Theor. Comput. Sci.",
- volume = "123",
+ "The connection between the motion of certain curves in $\mathbb{R}^3$
+ and $1+1$-dimensional soliton equations is by now well-established. On the
+ other hand, the sine-Gordon and other integrable equations may be
+ readily derived via the classical geometry of stationary
+ pseudospherical surfaces. Here, the motion of pseudospherical surfaces
+ $S$ is considered in a natural orthonormal triad formulation. In one case,
+ in a motion in which the Gaussian curvature of $S$ remains constant in
+ time, an integrable nonlinear evolution equation is derived which has
+ its origin in the description of wave propagation in an anharmonic
+ crystal. In a second case, wherein the Gaussian curvature is allowed
+ to vary in time, a classical generalised Weingarten system is derived
+ in connection with the purely normal propagation of a pseudospherical
+ surface. This is linked to triply orthogonal coordinate systems of
+ Bianchi type. The generalised Weingarten system incorporates an
+ integrable $2+1$-dimensional sine-Gordon equation. The arbitrariness of the
+ solutions of the generalised Weingarten system is determined via a
+ completion procedure."
+}
+
+\end{chunk}
+
+\index{Kajler, Norbert}
+\index{Soiffer, Neil}
+\begin{chunk}{axiom.bib}
+ author = "Kajler, Norbert and Soiffer, Neil",
+ title = "Some human interaction issues in computer algebra",
+ journal = "SIGSAM Bulletin",
+ volume = "28",
number = "1",
- pages = "117-130",
- year = "1994",
- keywords = "axiomref",
- abstract =
- "The paper deals with problems about conception and design of
- high-level computer algebra systems. Here we use a categorical
- approach given by the notion of sketches. Sketches allow to describe
- computation mechanisms in a syntactic way, well adapted to
- implementation.
-
- A computer algebra system must allow the manipulation of algebraic
- structures, in particular, the construction of new structures from
- known ones. In the paper we give a definition, at the sketch level, of
- parametrization of a structure by another one."
-}
-
-\end{chunk}
-
-\index{Duval, Dominique}
-\begin{chunk}{axiom.bib}
-@misc{Duva94e,
- author = "Duval, Dominique",
- title = "Symbolic or algebraic computation?",
- booktitle = "Publication du LACO",
- year = "1995",
- location = "Madrid Spain",
- comment = "NAG conference",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Duval, Dominique}
-\index{Reynaud, J.C.}
-\begin{chunk}{axiom.bib}
-@article{Duva94a,
- author = "Duval, D. and Reynaud, J.C.",
- title = "Sketches and Computation (Part I):
- Basic Definitions and Static Evaluation",
- journal = "Mathematical Structures in Computer Science",
- volume = "4",
- pages = "185-238",
- publisher = "Cambridge University Press",
- year = "1994",
- url = "http://journals.cambridge.org/abstract_S0960129500000438",
- paper = "Duva94a.pdf",
- abstract =
- "We define a categorical framework, based on the notion of {\sl
- sketch}, for specification and evaluation in the sense of algebraic
- specifications and algebraic programming. This framework goes far
- beyond our initial motivations, which was to specify computation with
- algebraic numbers. We begin by redefining sketches in order to deal
- explicitly with programs. Expressions and terms are carefully defined
- and studied, then {\sl quasi-projective sketches} are introduced. We
- describe {\sl static evaluation} in these sketches: we propose a
- rigorous basis for evaluation in the corresponding structures. These
- structures admit an initial model, but are not necessarily
- equational. In Part II (Duval and Reynaud 1994), we study a more
- general process, called {\sl dynamic evaluation}, for structures that
- may have no initial model."
-}
-
-\end{chunk}
-
-\index{Duval, Dominique}
-\index{Reynaud, Jean-Claude}
-\begin{chunk}{axiom.bib}
-@article{Duva94b,
- author = "Duval, Dominique and Reynaud, Jean-Claude",
- title = "Sketches and Computation (Part II):
- Dynamic Evaluation and Applications",
- journal = "Mathematical Structures in Computer Science",
- volume = "4",
- pages = "239-271",
- publisher = "Cambridge University Press",
- year = "1994",
- url = "http://journals.cambridge.org/abstract_S096012950000044X",
- paper = "Duva94b.pdf",
- abstract =
- "In the first part of this paper (Duval and Reynaud 1994), we defined a
- categorical framework, based on the notion of {\sl sketch}, for
- specification and evaluation in the senses of algebraic specification
- and algebraic programming. {\sl Static evaluation} in {\sl
- quasi-projective sketches} was defined in Part I; in this paper, {\sl
- dynamic evaluation} is introduced. It deals with more general
- structures, which may have no initial model. Until now, this process
- has not been used in algebraic specification systems, but computer
- algebra systems are beginning to use it as a basic tool. Finally, we
- give some applications of dynamic evaluation to computation in field
- extensions."
-}
-
-\end{chunk}
-
-\index{Duval, Dominique}
-\begin{chunk}{axiom.bib}
-@article{Duva94c,
- author = "Duval, Dominique",
- title = "Algebraic Numbers: An Example of Dynamic Evaluation",
- journal = "J. Symbolic Computation",
- volume = "18",
- pages = "429-445",
- year = "1994",
- url = "http://www.sciencedirect.com/science/article/pii/S0747717106000551",
- paper = "Duva94c.pdf",
- keywords = "axiomref",
- abstract = "
- Dynamic evaluation is presented through examples: computations
- involving algebraic numbers, automatic case discussion according to
- the characteristic of a field. Implementation questions are addressed
- too. Finally, branches are presented as ``dual'' to binary functions,
- according to the approach of sketch theory."
-}
-
-\end{chunk}
-
-\index{Duval, Dominique}
-\index{Reynaud, Jean-Claude}
-\begin{chunk}{axiom.bib}
-@article{Duva96,
- author = "Duval, D. and Reynaud, Jean-Claude",
- title = "Sketches and Computations over Fields",
- journal = "Mathematics and Computers in Simulation",
- volume = "42",
- pages = "363-373",
- year = "1996",
- paper = "Duva96.pdf",
- abstract =
- "The goal of this short paper is to describe one possible use of
- sketches in computer algebra. We show that sketches are a powerful
- tool for the description of mathematical structures and for the
- description of computations."
-}
-
-\end{chunk}
-
-\index{Duval, Dominique}
-\index{Gonz\'alez-Vega, L.}
-\begin{chunk}{axiom.bib}
-@article{Duva96a,
- author = {Duval, Dominique and Gonz\'alez-Vega, L.},
- title = "Dynamic Evaluation and Real Closure",
- journal = "Mathematics and Computers in Simulation",
- volume = "42",
- pages = "551-560",
- year = "1996",
- paper = "Duva96a.pdf",
- abstract = "
- The aim of this paper is to present how the dynamic evaluation method
- can be used to deal with the real closure of an ordered field. Two
- kinds of questions, or tests, may be asked in an ordered field:
- equality tests $(a=b?)$ and sign tests $(a > b?)$. Equality tests are
- handled through splittings, exactly as in the algebraic closure of a
- field. Sign tests are handled throug a structure called ``Tarski data
- type''."
-}
-
-\end{chunk}
-
-\index{Fritzson, D.}
-\index{Fritzson, P.}
-\index{Viklund, L.}
-\index{Herber, J.}
-\begin{chunk}{axiom.bib}
-@article{Frit94,
- author = "Fritzson, D. and Fritzson, P. and Viklund, L. and Herber, J.",
- title = "Object-oriented mathematical modelling - applied to machine
- elements",
- journal = "Comput. Struct.",
- volume = "51",
- number = "3",
- pages = "241-253",
+ pages = "18-28",
year = "1994",
- keywords = "axiomref",
- paper = "Frit94.pdf",
abstract =
- "Machine element analysis has a goal of describing function and other
- aspects of machine elements in a theoretical form. This paper shows
- how ideas from object-oriented modelling can be applied to machine
- elment analysis. The models thus obtained are both easier to
- understand, better structured, and allow a higher degree of re-use
- than conventional models. An object-oriented model description is
- natural and suitable for machine element analysis. As a realistic
- example an equational model of rolling bearings is presented. The
- structure of the model is general, and applies to many types of
- rolling bearings. The model and one solution require approximately
- 200+200 equations. The model is extensible, e.g. simple submodels of
- detailed properties can be made more complex without altering the
- overall structure. The example model has been implemented in a
- language of our own design. ObjectMath (Object-oriented Mathematical
- language for scientific computing). Using ObjectMath, it is possible
- to model classes of equation objects, to support multiple and single
- inheritance of equations, to support composition of equations, and to
- solve systems of equations. Algebraic transformations can conveniently
- be done since ObjectMath models are translated into the Mathematica
- computer algebra language. When necessary, equations can be
- transformed int C++ code for efficient numerical solution. The re-use
- of equations through inheritance reduced the size of the model by a
- factor of two, compared to a direct representation of the model in the
- Mathematica computer algebra language."
+ "This paper addresses some of the current issues concerning the
+ improvement of user interfaces for computer algebra systems. Some
+ state of the art commercial software as well as research prototypes
+ are presented, followed by a description of present research
+ directions."
}
\end{chunk}
-\index{Ioakimidis, N.I.}
+\index{Kripfganz, Jochen}
+\index{Perlt, Holger}
\begin{chunk}{axiom.bib}
-@article{Ioak94,
- author = "Ioakimidis, N.I.",
- title = "Symbolic computations for the solution of inverse/design
- problems with Maple",
- journal = "Comput. Struct.",
- volume = "53",
- number = "1",
- pages = "63-68",
+@misc{Krip94,
+ author = "Kripfganz, Jochen and Perlt, Holger",
+ title = "Working with Mathematica. An Introduction with examples",
+ comment = "Arbeiten mit Mathematica. Eine Einfuhrung mit Beispielen",
+ book = "Hander",
year = "1994",
keywords = "axiomref"
}
\end{chunk}
-\index{Jenks, Richard D.}
-\index{Trager, Barry M.}
+\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
-@InProceedings{Jenk94,
- author = "Jenks, Richard D. and Trager, Barry M.",
- title = "How to make AXIOM into a scratchpad",
- booktitle = "Proceedings of the ACM-SIGSAM 1989 International
- Symposium on Symbolic and Algebraic Computation, ISSAC '94",
- series = "ISSAC 94",
+@InProceedings{Schw94,
+ author = "Schwarz, Fritz",
+ title = "Computer algebra software for scientific applications",
+ booktitle = "Computerized symbolic manipulation in mechanics",
year = "1994",
- pages = "32-40",
- isbn = "0-89791-638-7",
- keywords = "axiomref",
- publisher = "ACM Press",
- address = "New York, NY, USA",
- paper = "Jenk94.pdf",
- abstract =
- "Scratchpad [GrJe71] was a computer algebra system developed in the
- early 1970s. Like M\&M (Maple [CGG91ab] and Mathematical [W01S92]) and
- other systems today, Scratchpad had one principal representation for
- mathematical formulae based on ``expression trees''. Its user interface
- design was based on a pattern-matching paradigm with infinite rewrite-
- rule semantics, providing what we believe to be the most natural
- paradigm for interactive symbolic problem solving. Like M\&M, however,
- user programs were interpreted, often resulting in poor performance
- relative to similar facilities coded in standard programming languages
- such as FORTRAN and C.
-
- Scratchpad development stopped in 1976 giving way to a new system
- design ([JenR79], [JeTr81]) that evolved into AXIOM [JeSu92].
- AXIOM has a strongly-typed programming language for building a library
- of parameterized types and algorithms, and a type-inferencing
- interpreter that accesses the library and can build any of an infinite
- number of types for interactive use.
-
- We suggest that the addition of an expression tree type to AXIOM can
- allow users to operate with the same freedom and convenience of
- untyped systems without giving up the expressive power and run-time
- efficiency provided by the type system. We also present a design that
- supports a multiplicity of programming styles, from the Scratchpad
- pattern-matching paradigm to functional programming to more
- conventional procedural programming. The resulting design seems to us
- to combine the best features of Scratchpad with current AXIOM and to
- offer a most attractive, flexible, and user-friendly environment for
- interactive problem solving.
-
- Section 2 is a discussion of design issues contrasting AXIOM with
- other symbolic systems. Sections 3 and 4 is an assessment of AXIOM’s
- current design for building libraries and interactive use. Section 5
- describes a new interface design for AXIOM, its resulting paradigms,
- and its underlying semantic model. Section 6 compares this work with
- others."
-}
-
-\end{chunk}
-
-\index{Bernard, Joey}
-\begin{chunk}{axiom.bib}
-@misc{Bern14,
- author = "Bernard, Joey",
- title = "Open Axiom",
- url = "http://www.linuxjournal.com/content/open-axiom",
- keywords = "axiomref",
- year = "2014"
-}
-
-\end{chunk}
-
-\index{Davenport, James H.}
-\index{Trager, Barry M.}
-\begin{chunk}{axiom.bib}
-@InProceedings{Dave90,
- author = "Davenport, James H. and Trager, Barry M.",
- title = "Scratchpad's view of algebra I: Basic commutative algebra",
- booktitle = "Design and Implementation of Symbolic Computation Systems",
- year = "1990",
- series = "DISCO '90",
- location = "Capri, Italy",
publisher = "Springer-Verlag",
- isbn = "0-387-52531-9",
- keywords = "axiomref",
- url = "http://opus.bath.ac.uk/32336/1/Davenport\_DISCO\_1990.pdf",
- paper = "Dave90.pdf",
- comment = "AXIOM Technical Report, ATR/1, NAG Ltd., Oxford, 1992",
+ pages = "67-117",
+ series = "CISM Courses Lecture 343",
keywords = "axiomref",
abstract =
- "While computer algebra systems have dealt with polynomials and
- rational functions with integer coefficients for many years, dealing
- with more general constructs from commutative algebra is a more recent
- problem. In this paper we explain how one system solves this problem,
- what types and operators it is necessary to introduce and, in short,
- how one can construct a computational theory of commutative
- algebra. Of necessity, such a theory is rather different from the
- conventional, non-constructive, theory. It is also somewhat different
- from the theories of Seidenberg [1974] and his school, who are not
- particularly concerned with practical questions of efficiency."
-}
-
-\end{chunk}
-
-\index{Jenks, Richard D.}
-\index{Trager, Barry M.}
-\begin{chunk}{axiom.bib}
-@article{Jenk81,
- author = "Jenks, Richard D. and Trager, Barry M.",
- title = "A Language for Computational Algebra",
- year = "1981",
- booktitle = "Proc. Symp. on Symbolic and Algebraic Manipulation",
- series = "SYMSAC 1981",
- location = "Snowbird, Utah",
- keywords = "axiomref",
- comment = "IBM Research Report 8930",
- abstract =
- "This paper reports ongoing research at the IBM Research Center on the
- development of a language with extensible parameterized types and
- generic operators for computational algebra. The language provides an
- abstract data type mechanism for defining algorithms which work in as
- general a setting as possible. The language is based on the notions of
- domains and categories. Domains represent algebraic
- structures. Categories designate collections of domains having common
- operations with stated mathematical properties. Domains and categories
- are computed objects which may be dynamically assigned to variables,
- passed as arguments, and returned by functions. Although the language
- has been carefully tailored for the application of algebraic
- computation, it actually provides a very general abstract data type
- mechanism. Our notion of a category to group domains with common
- properties appears novel among programming languages (cf. image
- functor of RUSSELL) and leads to a very powerful notion of abstract
- algorithms missing from other work on data types known to the authors."
-}
-
-\end{chunk}
-
-\index{Kapur, D.}
-\index{Musser, D.R.}
-\index{Stepanov, A.A.}
-\begin{chunk}{axiom.bib}
-@misc{Kapu81,
- author = "Kapur, D. and Musser, D.R. and Stepanov, A.A.",
- title = "Operators and Algebraic Structures",
- url = "http://www.stepanovpapers.com/p59-kapur.pdf",
- paper = "Kapu81.pdf",
- year = "1981",
- abstract =
- "Operators in functional languages such as APL and FFP are a useful
- programming concept. However, this concept cannot be ful- ly
- exploited in these languages because of certain constraints. It is
- proposed that an operator should be associated with a structure hav-
- ing the algebraic properties on which the operator's behavior depends.
- This is illustrated by introducing a language that provides mechanisms
- for defining structures and operators on them. Using this language,
- it is possible to describe algorithms abstractly, thus empliasizing
- the algebraic properties on which the algorithms depend. The role
- that formal representation of mathematical knowledge can play in the
- development of programs is illustrated through an example. An
- approach for associating complexity mea- sures with a structure and
- operators is also suggested. This ap- proach is useful in analyzing
- the complexity of algorithms in an abstract setting."
-}
-
-\end{chunk}
-
-\index{Jenks, Richard D.}
-\index{Sutor, Robert S.}
-\index{Watt, Stephen M.}
-\begin{chunk}{axiom.bib}
-@techreport{Jenk86,
- author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
- title = "Scratchpad II: An Abstract Datatype System for Mathematical
- Computation",
- institution = "IBM Research",
- year = "1986",
- type = "Research Report",
- number = "RC 12327 (\#55257)",
- url = "http://www.csd.uwo.ca/~watt/pub/reprints/1987-ima-spadadt.pdf",
- paper = "Jenk86.pdf",
- keywords = "axiomref",
- abstract = "
- Scratchpad II is an abstract datatype language and system that is
- under development in the Computer Algebra Group, Mathematical Sciences
- Department, at the IBM Thomas J. Watson Research Center. Some features
- of APL that made computation particularly elegant have been borrowed.
- Many different kinds of computational objects and data structures are
- provided. Facilities for computation include symbolic integration,
- differentiation, factorization, solution of equations and linear
- algebra. Code economy and modularity is achieved by having
- polymorphic packages of functions that may create datatypes. The use
- of categories makes these facilities as general as possible."
-}
-
-\end{chunk}
-
-\index{Lloyd, Michael}
-\index{Oancea, Cosmin}
-\index{Watt, Stephen}
-\begin{chunk}{axiom.bib}
-@misc{Chic04,
- author = "Chicha, Yannis and Lloyd, Michael Oancea, Cosmin",
- title = "Parametric Polymorphism for Computer Algebra Software Components",
- booktitle = "6th Int. Symp. on Symbolic and Numeric Algorithms for
- Scientific Computing",
- series = "SYNASC 04",
- location = "Imisoara, Romania",
- keywords = "axiomref",
- year = "2004",
- paper = "Chic04.pdf",
- url = "http://www.csd.uwo.ca/~watt/pub/reprints/2004-synasc-ppca.pdf",
+ "The central subject of this article are two basic questions: How to
+ make the process of developing computer algebra software on a large
+ scale ($10^4 to $10^5$) lines of code or more) more efficient and
+ how to improve the quality of the result. Taking procedures from well
+ established engineering sciences as a guide, two fundamental
+ principles turned out to be of overwhelming importance: Modularization
+ and limitation of growth through reuse. Important means for achieving
+ these goals turned out to be concept of an abstract data type and the
+ principles of object-oriented design. It is advocated to install an
+ additional abstraction level between the mathematics and the machine
+ in order to render it possible to develop (computer algebra) system
+ independent mathematical software. Basic constituents of this level
+ are a type system and a high-level language."
+}
+
+\end{chunk}
+
+\index{Kajler, Norbert}
+\begin{chunk}{axiom.bib}
+@article{Kajl92,
+ author = "Kajler, Norbert",
+ title = "CAS/PI: a Portable and Extensible Interface for Computer
+ Algebra Systems",
+ year = "1992",
+ booktitle = "Proc. ISSAC 1992",
+ series = "ISSAC 1992",
+ pages = "376-386",
+ isbn = "0-89791-489-9 (soft cover) 0-89791-490-2 (hard cover)",
+ keywords = "axiomref",
+ paper = "Kajl92.pdf",
abstract =
- "This paper presents our experiments in providing mechanisms for
- parametric polymorphism for computer algebra software components.
- Specific interfaces between Aldor and C++ and between Aldor and Maple
- are described. We then present a general solution, Generic IDL (GIDL),
- an extension to CORBA IDL supporting generic types. We describe our
- language bindings for C++, Java 1.5 and Aldor as well as aspects of
- our implementation, consisting of a GIDL to IDL compiler and tools for
- generating interface code for the various language bindings."
-}
-
-\end{chunk}
-
-\index{Watt, Stephen}
-\begin{chunk}{axiom.bib}
-@InProceedings{Watt07,
- author = "Watt, Stephen",
- title = "What Happened to Languages for Symolic Mathematical Computation?",
- booktitle = "Proc. Prog. Lang. for Mechanized Mathematics",
- series = "PLMMS 07",
- year = "2007",
- location = "RISC-Linz, Austria",
- pages = "81-90",
- keywords = "axiomref",
- paper = "Watt07.pdf",
+ "CAS/$\pi$ is a Computer Algebra System graphic user interface
+ designed to be highly portable and extensible. It has been developed
+ by composition of pre-existing software tools such as Maple, Sisyphe,
+ or Ulysse systems, ZicVis 3-D plotting library, etc, using control
+ integration technology and a set of high level graphic toolkits to
+ build the formula editor and the dialog manager. The main aim of
+ CAS/$\pi$ is to allow a wide range of runtime recon gurations and
+ extensions. For instance, it is possible to add new tools to a running
+ system, to modify connections between working tools, to extend the set
+ of graphic symbols managed by the formula editor, to design new high
+ level editing commands based on the syntax or semantics of
+ mathematical formulas, to customize and extend the menu-button based
+ user interface, etc. More generally, CAS/$\pi$ can be seen equally as
+ a powerful system-independent graphic user interface enabling
+ inter-systems communications, a toolkit to allow fast development of
+ custom-made scientific software environments, or a very convenient
+ framework for experimenting with computer algebra systems protocols
+ and man-machine interfaces."
+}
+
+\end{chunk}
+
+\index{Schu, J.}
+\index{Seiler, Werner Markus}
+\index{Calmet, Jacques}
+\begin{chunk}{axiom.bib}
+@InProceedings{Schu92,
+ author = "Schu, J. and Seiler, Werner Markus and Calmet, Jacques",
+ title = "Algorithmic Methods For Lie Pseudogroups'",
+ booktitle = "Proc. Modern Group Analysis: Advanced Analytical and
+ Computational Methods in Mathematical Physics",
+ pages = "337-344",
+ location = "Acireale (Italy)",
+ year = "1992",
+ publisher = "Kluwer",
url =
- "http://www.csd.uwo.ca/~watt/pub/reprints/2007-plmms-what\_happened.pdf",
- abstract =
- "While the state of the art is relatively sophisticated in programming
- language support for computer algebra, there has been less development
- in programming language support for symbolic computation over the past
- two decades. We summarize certain advances in programming languages
- for computer algebra and propose a set of directions and challenges
- for programming languages for symbolic computation."
-}
-
-\end{chunk}
-
-\index{Santas, Philip S.}
-\begin{chunk}{axiom.bib}
-@inproceedings{Sant96,
- author = "Santas, Philip S.",
- title = "Conditional Categories and Domains",
- keywords = "axiomref",
- booktitle = "Proc. DISCO 1996",
- year = "1996",
- pages = "112-125",
- isbn = "3-540-61697-7"
-}
-
-\end{chunk}
-
-
-\index{Santas, Philip S.}
-\begin{chunk}{axiom.bib}
-@book{Sant05,
- author = "Santas, Philip S.",
- title = "Conditional Categories and Domains",
- keywords = "axiomref",
- booktitle = "Design and Implementation of Symbolic Computation Systems",
- year = "2005",
- series = "Lecture Notes in Computer Science",
- volume = "1128",
- publisher = "Springer",
- abstract =
- "We extend the Type system defined in [Sant95] with Axiom-like
- Conditional Categories with the additional property of Static Typing
- and Checking. Categories and Domains may contain conditionals in their
- bodies, which are elaborated by our compiler by techniques used in
- standard typing. We define an appropriate calculus and discuss its
- properties. Examples inspired by the Axiom library illustrate the
- power of our apprach and its application in constructing algebraic
- concepts. The full calculus has been implemented and tested with our
- LA compiler which generated executable files."
-}
-
-\end{chunk}
-
-\begin{chunk}{axiom.bib}
-@misc{Gute16,
- author = "Gutenberg Self-Publishing Press",
- title = "OpenAxiom",
- keywords = "axiomref",
- url = "http://self.gutenberg.org/articles/openaxiom",
- year = "2016"
-}
-
-\end{chunk}
-
-\index{Baker, Martin}
-\begin{chunk}{axiom.bib}
-@misc{Bake16,
- author = "Baker, Martin",
- title = "Axiom Maths Program",
- keywords = "axiomref",
- year = "2016",
- url = "http://www.euclideanspace.com/prog/scratchpad/axiom/index.htm"
+ "http://www.iks.kti.edu/fileadmin/User/calmet/papers/Acireale-93.ps.gz",
+ keywords = "axiomref"
}
\end{chunk}
-\index{Caviness, Bob}
-\index{Trager, Barry}
-\index{Gianni, Patrizia}
+\index{Seiler, Werner Markus}
\begin{chunk}{axiom.bib}
-@misc{Cavi03,
- author = "Caviness, Bob and Trager, Barry and Gianni, Patrizia",
- title = "Dedicated to the Memory of Richard Dimick Jenks",
- year = "2003",
- url = "https://www.eecis.udel.edu/~caviness/jenks/issac-ded.pdf",
+@article{Seil99,
+ author = "Seiler, Werner Markus",
+ title = "DETools: A Library for Differential Equations",
+ paper = "Seil99.pdf",
+ year = "1999",
keywords = "axiomref",
- paper = "Cavi03.pdf",
abstract =
- "On December 30, 2003, Dick Jenks died at the age of 66, after an
- extended and courageous battle with multiple system atrophy.
-
- He received his PhD in mathematics from the University of Illinois at
- Urbana-Champaign in 1966. The title of his dissertation was
- “Quadratic Differential Systems for Mathematical Models” and was
- written under the supervision of Donald Gilles. After completing his
- PhD, he was a post-doctoral fellow at Brookhaven National Laboratory
- on Long Island. In 1968 he joined IBM Research where he worked until
- his retirement in 2002.
-
- At IBM he was one of the principal architects of the Scratchpad
- system, one of the earliest computer algebra systems(1971). Dick
- always believed that natural user interfaces were essential and
- developed a user-friendly rule-based system for Scratchpad. Although
- this rule-based approach was easy to use, as algorithms for computer
- algebra became more complicated, he began to understand that an
- abstract data type approach would give sophisticated algorithm
- development considerably more leverage. In 1977 he began the Axiom
- development (originally called Scratchpad II) with the design of
- MODLISP, a merger of Lisp with types (modes). In 1980, with the help
- of many others, he completed an initial prototype design based on
- categories and domains that were intended to be natural for
- mathematically sophisticated users.
-
- During this period many researchers in computer algebra visited IBM
- Research in Yorktown Heights and contributed to the development of
- the Axiom system. All this activity made the computer algebra group at
- IBM one of the leading centers for research in this area and Dick was
- always there to organize the visits and provide a stimulating and
- pleasant working environment for everyone. He had a good perspective
- on the most important research directions and worked to attract
- world-renowned experts to visit and interact with his group. He was an
- ideal manager for whom to work, one who always put the project and the
- needs of the group members first. It was a joy to work in such a
- vibrant and stimulating environment.
-
- After many years of development, a decision was made to rename
- Scratch- pad II to Axiom and to release it as a product. Dick and
- Robert Sutor were the primary authors of the book {\sl Axiom: The
- Scientific Computation System}. In the foreword of the book, written
- by David and Gregory Chudnovsky, it is stated that ``The Scratchpad
- system took its time to blossom into the beautiful Axiom
- product. There is no rival to this powerful environment in its scope
- and, most importantly, in its structure and organization.'' Axiom was
- recently made available as free software. See
- http://savannah.nongnu.org/projects/axiom
-
- Dick was active in service to the computer algebra community as
- well. Here are some highlights. He served as Chair of ACM SIGSAM
- (1979-81) and Conference Co-chair (with J. A. van Hulzen) of EUROSAM
- ’84, a precursor of the ISSAC meetings. Dick also had a long period of
- service on the editorial board of the {\sl Journal of Symbolic
- Computation}. At ISSAC ’95 in Montreal, Dick was elected to the
- initial ISSAC Steering Committee and was elected as the second Chair
- of the Committee in 1997. He, along with David Chudnovsky, organized
- the highly successful meetings on Computers and Mathematics that were
- held at Stanford in 1986 and MIT in 1989. As a legacy of those
- meetings, the Jenks Prize for outstanding contributions to software
- engineering in computer algebra has been established.
-
- Dick had many interests outside of his professional pursuits including
- reading, travel, physical fitness, and especially music. Dick was an
- accomplished pianist, organist, and vocalist. At one point he was the
- organist and choir master of the Church of the Holy Communion in
- Mahopac, NY. In the 1980s and 1990s, he sang in choral groups under
- the direction of Dr. Dennis Keene that performed at Lincoln Center in
- New York city.
-
- Personally, Dick was warm, generous, and outgoing with many
- friends. He will be missed for his technical accomplishments, his
- artist talents, and most of all for his positive, gentle, charming
- spirit."
+ "This article tries to give at least a brief introduction. The MuPAD
+ library is extended on two levels. The first one consists of a new
+ library detools containing a number of routines for treating
+ differential equations. This includes support for the graphical
+ presentation of the output of the numerical routines in MuPAD, some
+ methods for analysing or generating differential equations and also
+ routines for solving some classes of partial differential
+ equations. The use of this new library will be described in this
+ article. The second level is somewhat more advanced and requires a
+ certain familiarity with the object-oriented domains."
}
\end{chunk}
+\index{Bradford, Russell}
\index{Davenport, James H.}
-\index{Jenks, Richard D.}
-\begin{chunk}{axiom.bib}
-@article{Dave81,
- author = "Davenport, James H. and Jenks, Richard D.",
- title = "MODLISP",
- year = "1981",
- journal = "ACM SIGSAM Bulletin",
- volume = "15",
- issue = "1",
- pages = "11-20",
- publisher = "ACM",
- keywords = "axiomref",
+\index{England, Matthew}
+\index{McCallum, Scott}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Brad15,
+ author = "Bradford, Russell and Davenport, James H. and England, Matthew and
+ McCallum, Scott",
+ title = "Truth Table Invariant Cylindrical Algebraic Decomposition",
+ url = "https://arxiv.org/pdf/1401.0645.pdf",
+ paper = "Brad15.pdf",
+ year = "2015",
abstract =
- "This paper discusses the design and implementation of MODLISP, a
- LISP-like language enhanced with the idea of MODes. This extension
- permits, but does not require, the user to declare the types of
- various variables, and to compile functions with the arguments
- declared to be of a particular type. It is possible to declare several
- functions of the same name, with arguments of different type
- (e.g. PLUS could be declared for Integer arguments, or Rational, or
- Real, or even Polynomial arguments) and the system will apply the
- correct function for the types of the arguments."
-}
-
-\end{chunk}
-
-\index{Jenks, Richard D.}
-\begin{chunk}{axiom.bib}
-@inproceedings{Jenk79,
- author = "Jenks, Richard D.",
- title = "MODLISP: An Introduction",
- booktitle = "Proc. ISSAC 1979",
- series = "EUROSAM 79",
- pages = "466-480",
- year = "1979",
- publisher = "Springer-Verlag",
- isbn = "3-540-09519-5",
- comment = "IBM Research Report RC 8073 Jan 1980",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Davenport, James H.}
-\index{Jenks, Richard D.}
-\begin{chunk}{axiom.bib}
-@techreport{Dave80,
- author = "Davenport, James H. and Jenks, Richard D.",
- title = "MODLISP: A Preliminary Design",
- institution = "IBM Research",
- type = "Research Report",
- year = "1980",
- number = "RC 8073",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
+ "When using cylindrical algebraic decomposition (CAD) to solve a
+ problem with respect to a set of polynomials, it is likely not the
+ signs of those polynomials that are of paramount importance but rather
+ the truth values of certain quantifier free formulae involving
+ them. This observation motivates our article and definition of a Truth
+ Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors
+ presented an algorithm that can efficiently and directly construct a
+ TTICAD for a list of formulae in which each has an equational
+ constraint. This was achieved by generalising McCallum's theory of
+ reduced projection operators. In this paper we present an extended
+ version of our theory which can be applied to an arbitrary list of
+ formulae, achieving savings if at least one has an equational
+ constraint. We also explain how the theory of reduced projection
+ operators can allow for further improvements to the lifting phase of
+ CAD algorithms, even in the context of a single equational constraint.
+ The algorithm is implemented fully in Maple and we present both
+ promising results from experimentation and a complexity analysis
+ showing the benefits of our contributions."
+}
+
+\end{chunk}
+
+\index{Bradford, Russell}
+\index{Chen, Changbo}
\index{Davenport, James H.}
-\index{Jenks, Richard D.}
-\begin{chunk}{axiom.bib}
-@techreport{Dave80,
- author = "Davenport, James H. and Jenks, Richard D.",
- title = "MODLISP",
- institution = "IBM Research",
- type = "Research Report",
- year = "1980",
- number = "RC 8537 (\#37198)",
- keywords = "axiomref",
- comment = "http://www.computerhistory.org/collections/catalog/102719109"
-}
-
-\end{chunk}
-
-\index{Hoeven, Joris van der}
-\index{Lecerf, Gregoire}
-\begin{chunk}{axiom.bib}
-@misc{Hoev15,
- author = "Hoeven, Joris van der and Lecerf, Gregoire",
- title = "Interfacing Mathemagix with C++",
- keywords = "axiomref",
- url = "http://www.texmacs.org/joris/mmxcpp/mmxcpp.html",
- abstract =
- "In this paper, we give a detailed description of the interface
- between the Mathemagix language and C++. In particular, we describe
- the mechanism which allows us to import a C++ template library
- (which only permits static instantiation) as a fully generic
- Mathemagix template library."
-}
-
-\end{chunk}
-
-\index{Fortenbacher, A.}
-\index{Jenks, Richard}
-\index{Lucks, Michael}
-\index{Sutor, Robert}
-\index{Trager, Barry}
-\index{Watt, Stephen}
-\begin{chunk}{axiom.bib}
-@techreport{Fort85,
- author = "Fortenbacher, A. and Jenks, Richard and Lucks, Michael and
- Sutor, Robert and Trager, Barry and Watt, Stephen",
- title = "An Overview of the Scratchpad II Language and System",
- year = "1985",
- type = "Research Report",
- publisher = "IBM Research Computer Algebra Group",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\begin{chunk}{axiom.bib}
-@misc{Maxi16,
- author = "Maxima",
- title = "Other Free Computer Algebra Systems",
- url = "http://maxima.sourceforge.net/compalg.html",
- year = "2016",
- keywords = "axiomref",
- abstract =
- “Axiom is a general purpose Computer Algebra system. It is useful for
- doing mathematics by computer and for research and development of
- mathematical algorithms. It defines a strongly typed, mathematically
- correct type hierarchy. It has a programming language and a built-in
- compiler.
-
- There is also an interesting Rosetta Stone which offers translations
- of many basic operations for several computer algebra systems,
- including Maxima."
-}
-
-\end{chunk}
-
-\index{Jenks, Richard D.}
-\begin{chunk}{axiom.bib}
-@inproceedings{Jenk84b,
- author = "Jenks, Richard D.",
- title = "A primer: 11 keys to New Scratchpad",
- booktitle = "Proc. EUROSAM ISSAC 1984",
- year = "1984",
- publisher = "Springer-Verlag",
- pages = "123-147",
- isbn = "0-387-13350-X",
- keywords = "axiomref",
+\index{England, Matthew}
+\index{Maza, Marc Moreno}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Brad14,
+ author = "Bradford, Russell and Chen, Changbo and Davenport, James H. and
+ England, Matthew and Maza, Marc Moreno and Wilson, David",
+ title = "Truth Table Invariant Cylindrical Algebraic Decomposition by
+ Regular Chains",
+ url = "https://arxiv.org/pdf/1401.6310.pdf",
+ paper = "Brad14.pdf",
+ year = "2014",
abstract =
- "This paper is an abbreviated primer for the language of new
- SCRATCHPAD, a new implementation of SCRATCHPAD which has been under
- design and development by the Computer Algebra Group at the IBM
- Research Center during the past 6 years. The basic design goals of the
- new SCRATCHPAD language and interface to the user are to provde:
- \begin{itemize}
- \item a ``typeless'' interactive language suitable for on-line solution
- of mathematical problems by novice users with little or no programming
- required, and
- \item a programming language suitable for the formal description of
- algorithms and algebraic structures which can be compiled into run-time
- efficient object code.
- \end{itemize}
-
- The new SCRATCHPAD language is introduced by 11 keys with each
- successive key introducing an additional capability of the
- language. The language is thus described as a ``concentric'' language
- with each of the 11 levels corresponding to a language subset. These
- levels are more than just a pedagogic device, since they correspond to
- levels at which the system can be effectively used. Level 1 is
- sufficient for naive interactive use; levels 2-8 progressively
- introduce interactive users to capabilities of the language; levels
- 9-11 are for system programmers and advanced users. Levesl 2, 4, 6,
- and 7 give users the full power of LISP with a high-level language;
- level 8 introduces ``type declarations;'' level 9 allows polymorphic
- functions to be defined and compiled; levels 10-11 give users an
- Ada-like facility for defining types and packages (those of new
- SCRATCHPAD are dynamically constructable, however). One language is
- used for both interactive and system programming language use,
- although several freedomes such as abbreviation and optional
- type-declarations allowed at top-level are not permitted in system
- code. The interactive language (levels 1-8) is a blend of original
- SCRATCHPAD [GRJY75], some proposed extensions [JENK74], work by Loos
- [LOOS74], SETL [DEWA79], SMP [COWO81], and new ideas; the system
- programming language (levels 1-11) superficially resembles Ada but is
- more similar to CLU [LISK74] in its semantic design.
-
- This presentation of the language in this paper omits many details to
- be covered in the SCRATCHPAD System Programming Manual [SCRA84] and an
- expanded version of this paper will serve as a primer for SCRATCHPAD
- users [JESU84]."
+ "A new algorithm to compute cylindrical algebraic decompositions
+ (CADs) is presented, building on two recent advances. Firstly, the
+ output is truth table invariant (a TTICAD) meaning given formulae have
+ constant truth value on each cell of the decomposition. Secondly, the
+ computation uses regular chains theory to first build a cylindrical
+ decomposition of complex space (CCD) incrementally by polynomial.
+ Significant modification of the regular chains technology wa s used to
+ achieve the more sophisticated invariance criteria. Experimental
+ results on an implementation in the {\tt RegularChains} Library for Maple
+ verify that combining these advances gives an algorithm superior to
+ its individual components and competitive with the state of the art."
}
\end{chunk}
-\index{Griesmer, James H.}
-\index{Jenks, Richard D.}
-\index{Yun, David Y.Y}
-\begin{chunk}{axiom.bib}
-@techreport{Grie75,
- author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y",
- title = "SCRATCHPAD User's Manual",
- year = "1975",
- type = "Research Report",
- number = "RA70",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Jenks, Richard D.}
-\begin{chunk}{axiom.bib}
-@article{Jenk74,
- author = "Jenks, Richard D.",
- title = "The SCRATCHPAD language",
- journal = "ACM SIGPLAN Notices",
- comment = "reprinted in SIGSAM Bulletin, Vol 8, No. 2, May 1974",
- volume = "9",
- number = "4",
- pages = "101-111",
- year = "1974",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Jenks, Richard D.}
-\index{Sundaresan, Christine J.}
-\begin{chunk}{axiom.bib}
-@misc{Jenk84c,
- author = "Jenks, Richard D. and Sundaresan, Christine J.",
- title = "The 11 Keys to SCRATCHPAD: A Primer",
- year = "1984",
- keywords = "axiomref"
-}
-
+\index{Wilson, David}
+\index{Bradford, Russell}
\index{Davenport, James H.}
-\index{Gianni, Patrizia}
-\index{Jenks, Ricard D.}
-\index{Miller, Victor}
-\index{Morrison, Scott}
-\index{Rothstein, Michael}
-\index{Sundaresan, Christine J.}
-\index{Sutor, Robert S.}
-\index{Trager, Barry M.}
-\begin{chunk}{axiom.bib}
-@misc{Dave84b,
- author = "Davenport, James H. and Gianni, Patrizia and Jenks, Ricard D. and
- Miller, Victor and Morrison, Scott and Rothstein, Michael and
- Sundaresan, Christine J. and Sutor, Robert S. and Trager, Barry",
- title = "SCRATCHPAD System Programming Language Manual",
- year = "1984",
- keywords = "axiomref",
-}
-
-\end{chunk}
-
-\index{Constable, Robert L.}
-\index{Jackson, Paul B.}
-\begin{chunk}{axiom.bib}
-@misc{Cons98,
- author = "Constable, Robert L. and Jackson, Paul B.",
- title = "Towards Integrated Systems for Symbolic Algebra and Formal
- Constructive Mathematics",
- url = "http://www.nuprl.org/documents/Constable/towardsintegrated.pdf",
- paper = "Cons98.pdf",
- year = "1998",
+\index{England, Matthew}
+\begin{chunk}{axiom.bib}
+@misc{Wils14,
+ author = "Wilson, David and Bradford, Russell and Davenport, James H. and
+ England, Matthew",
+ title = "Cylindrical Algebraic Sub-Decompositions",
+ url = "https://arxiv.org/pdf/1401.0647.pdf",
+ paper = "Wils14.pdf",
+ year = "2014",
abstract =
- "The purpose of this paper is to report on our efforts to give e a
- formal account of some of the algebra used in Computer Algebra Systems
- (CAS). In particular, we look at the concepts used in the so called
- 3rd generation algebra systems, such as Axiom[4] and Weyl[9]. It is
- our claim that the Nuprl proof development system is especially well
- suited to support this kind of mathematics."
-}
-
-\end{chunk}
-
-\begin{chunk}{axiom.bib}
-@misc{Acad16,
- author = "Academic Search",
- title = "A Primer: 11 Keys to New Scratchpad",
- url =
- "http://libra.msra.cn/publication/645035/a-primer-11-keys-to-new-scratchpad",
- year = "2016",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Jenks, Richard D.}
-\begin{chunk}{axiom.bib}
-@misc{Jenk86a,
- author = "Jenks, Richard D.",
- title = "Basic Algebraic Facilities of the Scratchpad II Computer
- Algebra System",
- institution = "IBM Research",
- year = "1986",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Jenks, Richard D.}
-\begin{chunk}{axiom.bib}
-@misc{Jenk86b,
- author = "Jenks, Richard D.",
- title = "Scratchpad II Examples from INPUT files",
- institution = "IBM Research",
- year = "1986",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
+ "Cylindrical algebraic decompositions (CADs) are a key tool in real
+ algebraic geometry, used primarily for eliminating quantifiers over
+ the reals and studying semi-algebraic sets. In this paper we
+ introduce cylindrical algebraic sub-decompositions (sub-CADs), which
+ are subsets of CADs containing all the information needed to specify a
+ solution for a given problem. We define two new types of sub-CAD:
+ variety sub-CADs which are those cells in a CAD lying on a designated
+ variety; and layered sub-CADs which have only those cells of
+ dimension higher than a specified value. We present algorithms to
+ produce these and describe how the two approaches may be combined with
+ each other and the recent theory of truth-table invariant CAD. We
+ give a complexity analysis showing that these techniques can offer
+ substantial theoretical savings, which is supported by experimentation
+ using an implementation in Maple."
+}
+
+\end{chunk}
+
+\index{England, Matthew}
+\index{Wilson, David}
+\index{Bradford, Russell}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
-@article{Dave85,
- author = "Davenport, James H.",
- title = "The LISP/VM Foundation of Scratchpad II",
- journal = "The Scratchpad II Newsletter",
- volume = "1",
- number = "1",
- year = "1985",
- month = "September",
- institution = "IBM Research",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Wityak, Sandra}
-\begin{chunk}{ignore}
-@misc{Wity85,
- author = "Wityak, Sandra",
- title = "The Scratchpad II Newsletter",
- volume = "1",
- number = "1",
- year = "1985",
- month = "September",
- institution = "IBM Research",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Wityak, Sandra}
-\begin{chunk}{ignore}
-@misc{Wity86,
- author = "Wityak, Sandra",
- title = "The Scratchpad II Newsletter",
- volume = "1",
- number = "2",
- year = "1986",
- month = "January",
- institution = "IBM Research",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Wityak, Sandra}
-\begin{chunk}{ignore}
-@misc{Wity86a,
- author = "Wityak, Sandra",
- title = "The Scratchpad II Newsletter",
- volume = "1",
- number = "3",
- year = "1986",
- month = "May",
- institution = "IBM Research",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Watt, Stephen M.}
-\index{Jenks, Richard D.}
-\begin{chunk}{axiom.bib}
-@misc{Watt87,
- author = "Watt, Stephen M. and Jenks, Richard D.",
- title = "Abstract Datatypes, Multiple Views and Multiple Inheritance in
- Scratchpad II",
- keywords = "axiomref",
- year = "1987",
- url = "https://cs.uwaterloo.ca/~smatt/pub/reprints/1987-itl-spadviews.pdf",
- paper = "Watt87.pdf",
+@misc{Engl14,
+ author = "England, Matthew and Wilson, David and Bradford, Russell and
+ Davenport, James H.",
+ title = "Using the Regular Chains Library to build cylindrical algebraic
+ decompositions by projecting and lifting",
+ url = "https://arxiv.org/pdf/1405.6090.pdf",
+ paper = "Engl14.pdf",
+ year = "2014",
abstract =
- "Scratchpad II is an abstract datatype language developed at Yorktown
- Heights for the implementation of a new computer algebra system. It
- provides packages of polymorphic functions and parameterized, abstract
- datatypes with operator overloading and multiple inheritance. To
- express the intricate inter-relationships between the datatypes
- necessary for the description of mathematical objects, a number of
- techniques based on the notion of {\sl category} have been
- used. Categories are used to enforce relationships between type
- parameters and to provide the mechanism for multiple inheritance. They
- also allow the language to be statically type checked and the
- generation of efficient code. This paper describes the role of
- categories in Scratchpad II."
+ "Cylindrical algebraic decomposition (CAD) is an important tool, both
+ for quantifier elimination over the reals and a range of other
+ applications. Traditionally, a CAD is built through a process of
+ projection and lifting to move the problem within Euclidean spaces of
+ changing dimension. Recently, an alternative approach which first
+ decomposes complex space using triangular decomposition before
+ refining to real space has been introduced and implemented within the
+ Regular-Chains Library of Maple. We here describe a freely available
+ package ProjectionCAD which utilises the routines within the
+ RegularChains Library to build CADs by projection and lifting. We
+ detail how the projection and lifting algorithms were modified to
+ allow this, discuss the motivation and survey the functionality of the
+ package."
}
\end{chunk}
-\index{Watt, Stephen M.}
-\index{Jenks, Richard D.}
-\index{Sutor, Robert S.}
-\index{Trager, Barry M.}
-\begin{chunk}{axiom.bib}
-@inproceedings{Watt90,
- author = "Watt, Stephen M. and Jenks, Richard D. and Sutor, Robert S. and
- Trager, Barry M.",
- title = "The Scratchpad II type system: Domains and Subdomains",
- booktitle = "Computing Tools for Scientific Problem Solving",
- year = "1990",
- publisher = "Academic Press",
- url =
- "https://cs.uwaterloo.ca/~smwatt/pub/reprints/1990-miola-spadtypes.pdf",
- paper = "Watt90.pdf",
- keywords = "axiomref",
+\index{England, Matthew}
+\index{Bradford, Russell}
+\index{Davenport, James H.}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Engl14a,
+ author = "England, Matthew and Bradford, Russell and Davenport, James H. and
+ Wilson, David",
+ title = "Choosing a variable ordering for truth-table invariant cylindrical
+ algebraic decomposition by incremental triangular decomposition",
+ url = "https://arxiv.org/pdf/1405.6094.pdf",
+ paper = "Engl14a.pdf",
+ year = "2014",
abstract =
- "Scratchpad II is a language developed at Yorktown Heights for the
- implementation of a new computer algebra system. The need to model the
- intricate relationships among the datatypes representing mathematical
- objects has provided a number of challenges in the design of a type
- system for the programming language.
-
- In languages in which a datatype constructor may take multiple
- parameters, ensuring compatibility between them is extremely
- important. Scratchpad II addresses this issue by basing its
- implementation of abstract datatypes on {\cl categories}. Categories
- provide a convenient and useful method for specifying requirements on
- operations from datatypes. These requirements can be very complex when
- modelling mathematics.
-
- We show how categories provide multiple inheritance and how
- inheritance of specification is separated from inheritance of
- implementation. We also present implications of the type system on
- compilation of efficient code and flexibility of a weakly typed
- interactive user interface.
-
- Finally, the mechanisms of Scratchpad II are compared with those of
- traditional abstract datatype and object-oriented programming
- languages."
-}
-
-\end{chunk}
-
-\index{Zippel, Richard}
-\begin{chunk}{axiom.bib}
-@misc{Zipp93,
- author = "Zippel, Richard",
- title = "The Weyl Computer Algebra Substrate",
- paper = "Zipp93.pdf",
- keywords = "axiomref",
- booktitle = "Proc. of DISCO 1993",
- series = "DISCO 93",
- pages = "303=307",
- year = "1993"
+ "Cylindrical algebraic decomposition (CAD) is a key tool for solving
+ problems in real algebraic geometry and beyond. In recent years a new
+ approach has been developed, where regular chains technology is used
+ to first build a decomposition in complex space. We consider the
+ latest variant of this which builds the complex decomposition
+ incrementally by polynomial and produces CADs on whose cells a
+ sequence of formulae are truth-invariant. Like all CAD algorithms the
+ user must provide a variable ordering which can have a profound impact
+ on the tractability of a problem. We evaluate existing heuristics to
+ help with the choice for this algorithm, suggest improvements and then
+ derive a new heuristic more closely aligned with the mechanics of the
+ new algorithm."
}
\end{chunk}
-\index{Sutor, Robert S.}
-\begin{chunk}{axiom.bib}
-@inproceedings{Suto85,
- author = "Sutor, Robert S.",
- title = "The Scratchpad II computer algebra language and system",
- booktitle = "Research Contributions from the Euro. Conf. on Comp. Alg.",
- series = "Lecture Notes in Computer Science Volume 204",
- volume = "2",
- pages = "32-33",
- year = "1985",
- isbn = "0-387-15983-5 (vol. 1),0-387-15984-3 (vol. 2)",
- keywords = "axiomref"
-}
-
-\end{chunk}
-
-\index{Jenks, Richard D.}
-\begin{chunk}{axiom.bib}
-@article{Jenk88d,
- author = "Jenks, Richard D.",
- title = "Scratchpad II: A computer algebra language and system",
- journal = "The Journal of the Acoustical Society of America",
- year = "1988",
- volume = "83",
- number = "S1",
- pages = "S106",
- keywords = "axiomref",
+\index{England, Matthew}
+\index{Bradford, Russell}
+\index{Chen, Changbo}
+\index{Davenport, James H.}
+\index{Maza, Marc Moreno}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Engl14b,
+ author = "England, Matthew and Bradford, Russell and Chen, Changbo and
+ Davenport, James H. and Maza, Marc Moreno",
+ title = "Problem formulation for truth-table invariant cylindrical
+ algebraic decomposition by incremental triangular decomposition",
+ url = "https://arxiv.org/pdf/1404.6371.pdf",
+ paper = "Engl14b.pdf",
+ year = "2014",
abstract =
- "The Scratchpad II system represents a new generation of systems for
- doing symbolic mathematics, based on modern algebra and abstract data
- types. A large number of facilities are provided, for example:
- symbolic integration, ``infinite'' power series, differential operators,
- Cartesian tensors, and solution of nonlinear systems. Scratchpad II
- has been designed from the outset to be extendible. The system
- introduces a new data abstraction notion, the ``category,'' to express
- intricate interrelationships between data types. The result design
- permits the compilation of algorithms described in their most natural
- mathematical setting. The use of categories guarantees user defined
- types and packages are compatible with each other and with built in
- facilities. This system provides a single high‐level language with an
- intepreter and compiler. The language can be used by the naive user
- for convenient interactive mathematics calculations and by the
- advanced user for the efficient implementation of
- algorithms. Scratchpad II is built on Lisp/VM and runs on IBM/370
- class mainframes. An implementation of the system on the RT/PC is
- expected soon."
-}
-
-\end{chunk}
-
-\index{Jenks, Richard D.}
-\index{Sutor, Robert S.}
-\index{Watt, Stephen M.}
-\begin{chunk}{axiom.bib}
-@book{Jenk88e,
- author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
- title = "Scratchpad II: An Abstract Datatype System for Mathematical
- Computation",
- booktitle = "Mathematical Aspects of Scientific Software",
- year = "1988",
- pages = "157-182",
- publisher = "Springer",
- isbn = "0-387-18928-9",
- keywords = "axiomref",
+ "Cylindrical algebraic decompositions (CADs) are a key tool for
+ solving problems in real algebraic geometry and beyond. We recently
+ presented a new CAD algorithm combining two advances: truth-table
+ invariance, making the CAD invariant with respect to the truth of
+ logical formulae rather than the signs of polynomials; and CAD
+ construction by regular chains technology, where first a complex
+ decomposition is constructed by refining a tree incrementally by
+ constraint. We here consider how best to formulate problems for input
+ to this algorithm. We focus on a choice (not relevant for other CAD
+ algorithms) about the order in which constraints are presented. We
+ develop new heuristics to help make this choice and thus allow the
+ best use of the algorithm in practice. We also consider other choices
+ of problem formulation for CAD, as discussed in CICM 2013, revisiting
+ these in the context of the new algorithm."
+}
+
+\end{chunk}
+
+\index{Chen, Changbo}
+\index{Maza, Marc Moreno}
+\begin{chunk}{axiom.bib}
+@misc{Chen12,
+ author = "Chen, Changbo and Maza, Marc Moreno",
+ title = "An Incremental Algorithm for Computing Cylindrical Algebraic
+ Decompositions",
+ url = "https://arxiv.org/pdf/1210.5543.pdf",
+ paper = "Chen12.pdf",
+ year = "2012",
abstract =
- "Scratchpad II is an abstract datatype language and system that is
- under development in the Computer Algebra Group, Mathematical Sciences
- Department, at the IBM Thomas J. Watson Research Center. Many
- different kinds of computational objects and data structures are
- provided. Facilities for computation include symbolic integration,
- differentation, factorization, solution of equations and linear
- algebra. Code economy and modularity is achieved by having polymorphic
- packages of functions that may create datatypes. The use of categories
- makes these facilities as general as possible."
+ "In this paper, we propose an incremental algorithm for computing
+ cylindrical al gebraic decompositions. The algorithm consists of two
+ parts: computing a complex cylindrical tree and refining this complex
+ tree into a cylindrical tree in real space. The incrementality comes
+ from the first part of the algorithm, where a complex cylindrical tree
+ is constructed by refining a previous complex cylindrical tree with a
+ polynomial constraint. We have implemented our algorithm in Maple. The
+ experimentation shows that the proposed algorithm outperforms existing
+ ones for many examples taken from the literature"
}
\end{chunk}
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 2b68804..e751a9d 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -5454,6 +5454,8 @@ books/bookvol10.4 add Bronstein citations for LODE code
books/bookvolbib Axiom Citations in the Literature20160705.01.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160706.01.tpd.patch
+books/bookvolbib Axiom Citations in the Literature